The first five terms of a geometric sequence are 5, 10, 20, 40, 80.
A geometric sequence is also known as Geometric Progression (GP) is a non-zero numerical series whereby each term succeeding the very first is determined by multiplying the preceding one by a fixed, non-zero value designated as the common ratio.
It can be expressed by using the formula:
[tex]\mathbf{a_n = ar^{n-1}}[/tex]
where;
- [tex]\mathbf{a_n=}[/tex] [tex]\mathbf{n^{th}}[/tex] term of the sequence
- a = first term
- r = common ratio
Given that;
- the first term a₁ = 5
- the common ratio r = 2
∴
The second term of the sequence is:
[tex]\mathbf{a_2 = 5 \times 2^{2-1}}[/tex]
[tex]\mathbf{a_2 = 5 \times 2^{1}}[/tex]
[tex]\mathbf{a_2 = 10}[/tex]
The third term of the sequence is:
[tex]\mathbf{a_3 = 5 \times 2^{3-1}}[/tex]
[tex]\mathbf{a_3 = 5 \times 2^{2}}[/tex]
[tex]\mathbf{a_2 = 20}[/tex]
The fourth term of the sequence is:
[tex]\mathbf{a_4 = 5 \times 2^{4-1}}[/tex]
[tex]\mathbf{a_3 = 5 \times 2^{3}}[/tex]
[tex]\mathbf{a_4 = 40}[/tex]
The fifth term of the sequence is:
[tex]\mathbf{a_5 = 5 \times 2^{5-1}}[/tex]
[tex]\mathbf{a_3 = 5 \times 2^{4}}[/tex]
[tex]\mathbf{a_4 = 80}[/tex]
Learn more about the Geometric sequence here:
https://brainly.com/question/1509142
